Installing toolboxes and setting up the path.

You need to unzip these toolboxes in your working directory, so that you have toolbox_signal and toolbox_general in your directory.

For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.

Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.

where \(J(u)\) is a cartoon image prior (that favors edges) and \(T(v)\) is a texture image prior (that favors oscillations).
The parameters \(\lambda,\mu\) should be adapted to the noise level and the amount of edge/textures.

When no noise is present in \(f\), so that \(w^\star=0\), on minimizes \[ \min_{u} \: T(f-u) + \lambda J(u). \]

In this tour, we define \(J\) as the total variation prior. For \(T\), we use the Hilbert norm framework introduced in:

Gabor Hilbert Energy

To model the texture, one should use a prior \(T(v)\) that favors oscillations. We thus use a weighted \(L^2\) norms computed
over the Fourier domain: \[ T(v) = \frac{1}{2} \sum_{\omega} \|W_{\omega} \hat f(\omega) \|^2 \] where \(W_\omega\) is the
weight associated to the frequency \(\omega\).